Journal of Commutative Algebra

Lattice complements and the subadditivity of syzygies of simplicial forests

Sara Faridi

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Abstract

We prove the subadditivity property for the maximal degrees of the syzygies of facet ideals of simplicial forests. We do this by interpreting the subadditivity property for any monomial ideal as a property of homologies of its lcm lattice. For an ideal $I$ that is the facet ideal of a simplicial forest, if the $i$-th Betti number is nonzero and $i=a+b$, we show that there are monomials in the lcm lattice of $I$ that are complements in part of the lattice, each supporting a nonvanishing $a$-th and $b$-th Betti number. The subadditivity formula follows from this fact.

Article information

Source
J. Commut. Algebra, Volume 11, Number 4 (2019), 535-546.

Dates
First available in Project Euclid: 7 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.jca/1575687733

Digital Object Identifier
doi:10.1216/JCA-2019-11-4-535

Mathematical Reviews number (MathSciNet)
MR4039981

Zentralblatt MATH identifier
07147395

Subjects
Primary: 13D02: Syzygies, resolutions, complexes

Keywords
Monomial ideals lattice complements resolutions syzygies simplicial forests

Citation

Faridi, Sara. Lattice complements and the subadditivity of syzygies of simplicial forests. J. Commut. Algebra 11 (2019), no. 4, 535--546. doi:10.1216/JCA-2019-11-4-535. https://projecteuclid.org/euclid.jca/1575687733


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References

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